Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	2^331110+1870459	99675	Enzo Doria	05/2016
9752	5*2^331075+7	99665	Lelio R Paula	08/2014
9753	25776^7351+7351^25776	99659	Hans Havermann	02/2018
9754	(16*10^99656-31)/3	99657	Robert Price	03/2016
9755	(6059^26347-1)/6058	99652	Serge Batalov	06/2022
9756	(15544^23773-1)/15543	99642	Serge Batalov	06/2022
9758	2^330968+345	99632	Lelio R Paula	09/2016
9757	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
9760	2*5^142528-7	99624	Lelio R Paula	11/2014
9759	2^330942+77329	99624	Enzo Doria	05/2016
9761	14^86914-99	99615	Lelio R Paula	08/2016
9762	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
9763	22971^21692+21692^22971	99610	Hans Havermann	03/2018
9764	2^330845+71687	99595	Enzo Doria	04/2016
9765	(26667^22501-1)/26666	99585	Serge Batalov	06/2022
9766	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
9767	24494^11613+11613^24494	99567	Hans Havermann	03/2018
9768	2^330735+8415	99562	Lelio R Paula	09/2016
9769	2^330720+74071	99557	Enzo Doria	04/2016
9770	(10405^24781-1)/10404	99548	Serge Batalov	06/2022
9772	31^66738-2	99531	Lelio R Paula	09/2013
9771	(9002^25171-1)/9001	99531	Serge Batalov	06/2022
9773	(5023^26893-1)/5022	99527	Serge Batalov	06/2022
9774	7*3^208567+4	99513	Lelio R Paula	08/2014
9775	(15881^23689-1)/15880	99511	Serge Batalov	06/2022
9776	(13*10^99508+47)/3	99509	Robert Price	01/2017
9777	2^330553+779	99507	Lelio R Paula	01/2013
9778	15^84606-94	99505	Lelio R Paula	08/2016
9779	(10^99497+173)/3	99497	Robert Price	05/2021
9780	9*10^99493-43	99494	Robert Price	09/2021
9781	6^127858+47	99493	Lelio R Paula	08/2016
9782	5^142337+48	99490	Lelio R Paula	08/2016
9783	7^117724-20	99489	Lelio R Paula	08/2016
9784	(559^36209-1)/558	99479	Serge Batalov	06/2022
9785	(13470^24091-1)/13469	99477	Serge Batalov	06/2022
9786	(29*10^99474-17)/3	99475	Erik Branger	09/2014
9787	(185*10^99466-11)/3	99468	Robert Price	10/2020
9788	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
9789	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
9790	(516*32^66077-175)/31	99458	Eric Chen	04/2023
9791	(2863^28771-1)/2862	99453	Serge Batalov	06/2022
9792	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
9793	179^44142-44142^179	99446	Norman Luhn	08/2024
9794	(68*10^99441+7)/3	99443	Robert Price	03/2016
9795	10^99434+155571	99435	Patrick De Geest	04/2020
9796	10^99434-123456789	99434	Robert Price	02/2020
9797	10^99434-191237	99434	Patrick De Geest	04/2020
9798	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
9799	23839^14802+14802^23839	99417	Hans Havermann	02/2018
9800	(2*10^99408+529)/9	99408	Robert Price	01/2017
9801	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
9802	53^57646-2	99398	Lelio R Paula	09/2013
9803	2^330165+1870025	99390	Enzo Doria	05/2016
9804	7*10^99383+97	99384	Robert Price	09/2021
9805	2^330142-155	99383	Lelio R Paula	12/2012
9806	2^330088-115259	99367	Enzo Doria	06/2015
9807	24216^12671+12671^24216	99354	Hans Havermann	01/2018
9808	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
9809	(746*10^99303+1)/9	99305	Robert Price	02/2017
9810	3^208107+40	99293	Lelio R Paula	08/2016
9811	2^329843+211343	99293	Enzo Doria	08/2023
9812	(3939^27617-1)/3938	99291	Serge Batalov	06/2022
9813	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
9814	8*3^208093+5	99287	Lelio R Paula	08/2014
9815	5^142043+56	99284	Lelio R Paula	08/2016
9816	(13*10^99282-157)/9	99283	Robert Price	05/2021
9817	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
9818	22*10^99275+7	99277	Robert Price	04/2016
9819	2^329778+1876189	99274	Enzo Doria	07/2016
9820	(149557^19321-1)/(149557^139-1)	99264	Ryan Propper	11/2023
9821	(6580^25997-1)/6579	99259	Serge Batalov	06/2022
9822	(2249^29611-1)/2248	99253	Serge Batalov	06/2022
9823	(10^99239-13)/3	99239	Robert Price	02/2017
9824	(1199^32233-1)/1198	99237	Serge Batalov	06/2022
9826	3^207987+62	99236	Lelio R Paula	08/2016
9825	(62*10^99235+91)/9	99236	Robert Price	07/2021
9827	2^329638+49	99231	Lelio R Paula	12/2012
9828	7^117413-18	99226	Lelio R Paula	08/2016
9829	2^329586-458903	99216	Enzo Doria	04/2015
9830	(6290^26119-1)/6289	99214	Serge Batalov	06/2022
9832	2^329553+101	99206	Lelio R Paula	12/2012
9831	(21297^22921-1)/21296	99206	Serge Batalov	06/2022
9833	2^329551-112897	99205	Enzo Doria	06/2014
9834	(3^207925+7)/50	99204	Lelio R Paula	09/2013
9835	U(477331)/57279721	99202	Serge Batalov	07/2024
9836	6^127458-17993	99182	Enzo Doria	03/2013
9837	27197^4428+4428^27197	99166	Hans Havermann	10/2017
9838	(46*10^99143-1)/9	99144	Robert Price	12/2014
9839	(64*10^99135+161)/9	99136	Robert Price	08/2022
9840	7*10^99133+69	99134	Robert Price	10/2017
9841	(21701^22861-1)/21700	99132	Serge Batalov	06/2022
9842	18^78968-3065	99127	Enzo Doria	03/2013
9843	25927^6654+6654^25927	99122	Hans Havermann	10/2017
9844	87915!4+16	99122	Robert Price	09/2019
9845	2^329259+189	99117	Lelio R Paula	12/2012
9846	8*10^99113+39	99114	Robert Price	01/2017
9847	6^127364+77	99109	Lelio R Paula	08/2016
9848	(82*10^99103+143)/9	99104	Robert Price	06/2021
9849	(11414^24421-1)/11413	99083	Serge Batalov	06/2022
9850	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
9851	(22089^22807-1)/22088	99074	Serge Batalov	06/2022
9852	(59*10^99069+391)/9	99070	Robert Price	03/2021
9853	(797*10^99061-41)/9	99063	Robert Price	04/2022
9854	2^329058-287681	99057	Harrison Mesh	06/2022
9855	6^127285+13	99047	Lelio R Paula	08/2016
9856	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
9857	2^329007+73283	99041	Enzo Doria	04/2016
9858	(145413^19321-1)/(145413^139-1)	99030	Ryan Propper	11/2023
9859	5*3^207543-8	99024	Lelio R Paula	08/2014
9860	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
9861	2^328885+149	99005	Lelio R Paula	12/2012
9862	23392^17075+17075^23392	99004	Hans Havermann	09/2017
9863	(7424^25579-1)/7423	99004	Serge Batalov	06/2022
9864	(2^328879-9)/119	99001	Lelio R Paula	10/2013
9865	140^46129-46129^140	98999	Norman Luhn	08/2024
9866	169^44432-44432^169	98990	Norman Luhn	08/2024
9867	5^141618+54	98987	Lelio R Paula	08/2016
9868	2^328824+24391	98986	Enzo Doria	10/2023
9869	8*10^98982+51	98983	Robert Price	05/2017
9870	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
9871	2^328794-2797601	98977	Enzo Doria	04/2016
9872	(88331^20011-1)/88330	98972	Serge Batalov	06/2022
9873	6^127176+5	98963	Lelio R Paula	11/2014
9874	2*10^98961-21	98962	Robert Price	09/2020
9875	24262^11989+11989^24262	98960	Hans Havermann	09/2017
9876	(60138^20707-1)/60137	98958	Serge Batalov	06/2022
9877	2^328700-109709	98949	Enzo Doria	04/2014
9878	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
9879	(1014^32917-1)/1013	98947	Serge Batalov	06/2022
9880	87771!4-128	98944	Robert Price	11/2019
9881	(4576^27031-1)/4575	98943	Serge Batalov	06/2022
9882	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
9883	(1933^30103-1)/1932	98923	Serge Batalov	06/2022
9884	46711!2-2^46711	98916	Robert Price	09/2015
9885	9*7^117037+4	98909	Lelio R Paula	11/2014
9886	127^47012+126	98905	Norbert Schneider	01/2019
9887	(93826^19891-1)/93825	98900	Serge Batalov	06/2022
9889	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
9888	2^328524+625	98896	Henri Lifchitz	09/2024
9890	(10^98890+149)/3	98890	Serge Batalov	12/2014
9891	22775^21978+21978^22775	98889	Hans Havermann	08/2017
9892	2^328497-216933	98888	Enzo Doria	05/2014
9893	2^328487+32769	98885	Lelio R Paula	08/2016
9894	3^207250-112358	98884	Enzo Doria	06/2014
9895	13^88754-90	98867	Lelio R Paula	08/2016
9896	2^328406+709	98861	Lelio R Paula	02/2013
9897	2*10^98860-21	98861	Robert Price	09/2020
9898	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
9899	7^116976+76	98857	Lelio R Paula	08/2016
9900	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
9901	(25411^22441-1)/25410	98849	Serge Batalov	06/2022
9902	(18668^23143-1)/18667	98842	Serge Batalov	06/2022
9904	2^328335+1155	98839	Lelio R Paula	08/2016
9903	2^328333-349003	98839	Harrison Mesh	06/2022
9906	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
9905	287^40210+40210^287	98832	Norbert Schneider	11/2014
9907	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
9908	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
9909	(28623^22171-1)/28622	98806	Serge Batalov	06/2022
9910	24746^9825+9825^24746	98795	Hans Havermann	07/2020
9911	26620^5143+5143^26620	98793	Hans Havermann	07/2020
9912	65^54491+48	98788	Lelio R Paula	04/2016
9913	3^207042+98	98785	Lelio R Paula	08/2016
9914	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
9915	10^98754+73383	98755	Patrick De Geest	02/2021
9918	3^206977-112756	98754	Enzo Doria	07/2014
9917	10^98754-40000000001	98754	Robert Price	09/2020
9916	10^98754-169343	98754	Patrick De Geest	02/2021
9919	7^116846-50	98747	Lelio R Paula	08/2016
9920	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
9921	23267^17512+17512^23267	98730	Hans Havermann	04/2020
9922	2^327967-28635	98728	Lelio R Paula	08/2016
9923	707^34642+34642^707	98710	Norbert Schneider	12/2017
9924	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
9925	6^126850-47	98709	Lelio R Paula	08/2016
9926	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
9927	(22*10^98697+47)/3	98698	Robert Price	06/2021
9928	(139706^19321-1)/(139706^139-1)	98696	Ryan Propper	11/2023
9929	8*6^126830-7	98694	Lelio R Paula	11/2014
9930	11^94770-270	98693	Enzo Doria	08/2012
9931	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
9932	2^327832+43	98688	Lelio R Paula	12/2012
9933	2^327795+761	98677	Lelio R Paula	02/2013
9934	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
9935	10^98669+147411	98670	Patrick De Geest	11/2016
9937	10^98669-9^(98669-1)	98669	Robert Price	05/2016
9936	10^98669-105249	98669	Patrick De Geest	11/2016
9938	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
9939	2^327671-109801	98639	Enzo Doria	04/2014
9940	24398^11037+11037^24398	98638	Hans Havermann	10/2019
9941	5^141090-14	98618	Lelio R Paula	08/2016
9942	20^75799+47	98617	Lelio R Paula	08/2016
9943	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
9944	28101^3226+3226^28101	98597	Hans Havermann	07/2020
9945	2^327515-1017	98592	Lelio R Paula	08/2016
9946	6^126692+97681	98586	Mike Oakes	04/2011
9947	2^327467-741	98578	Lelio R Paula	08/2016
9948	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
9949	22713^21800+21800^22713	98540	Hans Havermann	05/2020
9950	(2^327329+9)/19	98535	Lelio R Paula	10/2013
9951	7^116577-66	98519	Lelio R Paula	08/2016
9952	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
9953	23220^17479+17479^23220	98512	Hans Havermann	03/2020
9954	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
9955	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
9956	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
9957	2^327162-66945	98486	Lelio R Paula	08/2016
9958	30139^1852+1852^30139	98484	Hans Havermann	02/2020
9959	23182^17703+17703^23182	98479	Hans Havermann	01/2020
9960	4*10^98472-3	98473	Erik Branger	11/2013
9961	26167^5794+5794^26167	98466	Hans Havermann	01/2020
9962	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
9963	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
9964	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
9965	13^88363+94	98432	Lelio R Paula	08/2016
9966	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
9967	6^126481+41	98422	Lelio R Paula	08/2016
9968	78*10^98413-7	98415	Robert Price	05/2017
9969	22634^22263+22263^22634	98404	Hans Havermann	07/2020
9970	(47*10^98386+241)/9	98387	Robert Price	06/2022
9971	7^116416+46	98383	Lelio R Paula	08/2016
9972	7^116407-24	98376	Lelio R Paula	07/2016
9973	439^37228+37228^439	98374	Norbert Schneider	08/2018
9974	2^326782-1860671	98372	Enzo Doria	03/2016
9975	17^79948+58	98372	Lelio R Paula	08/2016
9976	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
9977	3^206143-98	98356	Lelio R Paula	08/2016
9978	8*5^140705+7	98350	Lelio R Paula	11/2014
9979	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
9980	(638^35053-1)/637	98315	Serge Batalov	06/2022
9981	2^326585+11	98312	Lelio R Paula	12/2012
9982	2^326582-459161	98311	Enzo Doria	05/2015
9983	(1266^31687-1)/1265	98304	Serge Batalov	06/2022
9985	(2^326548+9)/5	98301	Lelio R Paula	10/2013
9984	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
9986	2^326538+71659	98298	Enzo Doria	04/2016
9987	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
9988	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
9989	15^83575-58	98292	Lelio R Paula	08/2016
9990	10^98288+3	98289	Robert Price	03/2011
9991	10^98288-117017	98288	Patrick De Geest	11/2011
9992	(44*10^98284-719)/9	98285	Robert Price	12/2017
9993	(5985^26021-1)/5984	98280	Serge Batalov	06/2022
9994	23466^15419+15419^23466	98277	Hans Havermann	02/2020
9995	2^326421-2797573	98263	Enzo Doria	04/2016
9996	2^326401+16095	98257	Lelio R Paula	07/2016
9997	(6494^25771-1)/6493	98249	Serge Batalov	06/2022
9998	7^116240-116240^7	98235	Norbert Schneider	05/2017
9999	17^79826-78	98222	Lelio R Paula	08/2016
10000	2^326268-809	98217	Yves Minet	04/2011

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Probable Primes Top 10000

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